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Maths GCSE Paper Revision (Transformations (Enlargement (To find the scale…
Maths GCSE Paper Revision
Congruent Shapes
If a two shapes, (e.g a triangle) are
Congruent
, it means they are
identical
to one another. They have the same length of sides; same angles. If a shape is identical to another, it has
Congruency
with that shape.
e.g
.
In this picture, shapes
D and I
are
congruent
to each other, because they are the same size, each have one angle, and have have one side which are the same lengths, therefore are identical.
Geometric Progression
A
Geometric Progression
(also known as a
Geometric Sequence
) is a sequence of numbers in which each term (number) after the first is found by multiplying the previous one by a fixed, non-zero number called the
common ratio
.
e.g.
2, 6, 18, 54
- the
common ratio
of this sequence is
3
, because each number is multiplied by three to get the next number in the sequence.
Standard Index Form
Standard Index Form
is also known as
Standard Form
. If in a question you are asked to write something in standard form, it
always
means to write out the number given as:
a x 10 to a power.
You would usually use index numbers (standard form) to write out a particularly
big
number.
e.g.
15, 000, 000
, is basically,
1.5 x 10 x 10 x 10 x 10 x 10 x 10 x 10
, therefore written out in index form, would be
1.5 x 10 to the power of 7
, because 1.5 is being multiplied by
7 lots of ten
.
Prime Factors
If you are asked in a question to break a number down into it's
prime factors
, or to write the number in prime factors, it means to break a number down using a
tree diagram,
into the smallest numbers it is until all the numbers left multiplying each other are
prime numbers
.
e.g.
2 x 3 x 2 x 2 = 24
QUESTION EXAMPLE:
A:
4,8,9,14,15,19 etc.
Q:
Give an example to show that
n
(as a whole number) in this equation does not equal a
prime number.
6n + 1
.
Explained:
This question is basically asking you to list some numbers which if were the value of
n
in the equation above, which
Transformations
Enlargement
To find the
scale factor of enlargement
, you divide the new length of one side of the triangle, by the old length of the side of the triangle (before it was enlarged)
e.g
.
In this photo, the smaller equilateral triangle has been enlarged by scale factor 3, because the larger equilateral triangle has a side length of 15, so 15 divided by 9 = 15/9, which equals 5/3.
Reflection
The mirror line is the line which the two shapes are reflected.
Without taking notice of the grid, you write the equation of the line the shapes are reflected, e.g. in this picture, the equation is y = -1, because the mirror line is horizontal going through -1y.
Translation
Rotation
To answer a question which asks you 'what transformation has taken place on this grid' or something similar, you will be given a picture also of the shape, and if it is a rotation you would answer:
'Rotation clockwise/anti-clockwise
s
degrees at point
(x,x)
Pythagoras
